Under different operating parameters and gas/solid physical properties, the pressure drop distribution, the cavity and pinning phenomena in the rectangular cross-flow moving bed are investigated by the Eulerian two-fluid & the kinetic theory of granular flow models with single variable method. The simulation results are validated by the experimental data. The particle force equations are built to explain the occurrence mechanisms of the cavity and pinning phenomena. For describing the pressure drop distribution more explicitly, the bed average pressure drop and the radial uneven index of pressure drop (UI) are introduced. In addition, the combined body force is introduced to explain the influences of different parameters and properties on the cavity and pinning phenomena. The relative deformation of particle group is also applied to analyze the cavity/pinning sizes under different particle packing properties. (C) 2017 Published by Elsevier B.V.